Answer :
To solve the problem, let's start by breaking down the given information into an equation.
You have a number [tex]\( n \)[/tex].
Three times this number would be represented as [tex]\( 3n \)[/tex].
Then, the problem states "15 less than 3 times itself," so that's [tex]\( 3n - 15 \)[/tex].
Next, you are to add [tex]\( n \)[/tex] to this expression. So the equation becomes:
[tex]\[ n + (3n - 15) = 101 \][/tex]
Let's simplify this step-by-step:
1. Start with the expression:
[tex]\[ n + (3n - 15) = 101 \][/tex]
2. Combine like terms:
[tex]\[ n + 3n - 15 = 101 \][/tex]
[tex]\[ 4n - 15 = 101 \][/tex]
3. To isolate [tex]\( n \)[/tex], add 15 to both sides of the equation:
[tex]\[ 4n - 15 + 15 = 101 + 15 \][/tex]
[tex]\[ 4n = 116 \][/tex]
4. Finally, divide both sides by 4:
[tex]\[ n = \frac{116}{4} \][/tex]
[tex]\[ n = 29 \][/tex]
Therefore, the correct equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
Hence, the correct equation choice is:
[tex]\[ \boxed{3n - 15 + n = 101} \][/tex]
You have a number [tex]\( n \)[/tex].
Three times this number would be represented as [tex]\( 3n \)[/tex].
Then, the problem states "15 less than 3 times itself," so that's [tex]\( 3n - 15 \)[/tex].
Next, you are to add [tex]\( n \)[/tex] to this expression. So the equation becomes:
[tex]\[ n + (3n - 15) = 101 \][/tex]
Let's simplify this step-by-step:
1. Start with the expression:
[tex]\[ n + (3n - 15) = 101 \][/tex]
2. Combine like terms:
[tex]\[ n + 3n - 15 = 101 \][/tex]
[tex]\[ 4n - 15 = 101 \][/tex]
3. To isolate [tex]\( n \)[/tex], add 15 to both sides of the equation:
[tex]\[ 4n - 15 + 15 = 101 + 15 \][/tex]
[tex]\[ 4n = 116 \][/tex]
4. Finally, divide both sides by 4:
[tex]\[ n = \frac{116}{4} \][/tex]
[tex]\[ n = 29 \][/tex]
Therefore, the correct equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
Hence, the correct equation choice is:
[tex]\[ \boxed{3n - 15 + n = 101} \][/tex]
